# Magnificent Mistakes in Mathematics

Two veteran math educators demonstrate how some "magnificent mistakes" had profound consequences for our understanding of mathematics' key concepts.

In the nineteenth century, English mathematician William Shanks spent fifteen years calculating the value of pi, setting a record for the number of decimal places. Later, his calculation was reproduced

## Overview

Two veteran math educators demonstrate how some "magnificent mistakes" had profound consequences for our understanding of mathematics' key concepts.

In the nineteenth century, English mathematician William Shanks spent fifteen years calculating the value of pi, setting a record for the number of decimal places. Later, his calculation was reproduced using large wooden numerals to decorate the cupola of a hall in the Palais de la Découverte in Paris. However, in 1946, with the aid of a mechanical desk calculator that ran for seventy hours, it was discovered that there was a mistake in the 528th decimal place. Today, supercomputers have determined the value of pi to trillions of decimal places.

This is just one of the amusing and intriguing stories about mistakes in mathematics in this layperson's guide to mathematical principles. In another example, the authors show that when we "prove" that every triangle is isosceles, we are violating a concept not even known to Euclid - that of "betweenness." And if we disregard the time-honored Pythagorean theorem, this is a misuse of the concept of infinity. Even using correct procedures can sometimes lead to absurd - but enlightening - results.

Requiring no more than high-school-level math competency, this playful excursion through the nuances of math will give you a better grasp of this fundamental, all-important science.

From the Hardcover edition.

## Editorial Reviews

Library Journal
Posamentier (mathematics education, Mercy Coll.) and Lehmann (formerly, mathematics, Humboldt Univ., Berlin), coauthors of several math books, present a compendium of mathematical errors, arranged by topic into five chapters. Only the first, on errors made by eminent mathematicians, has much narrative. Here, we see number-theoretic conjectures that were based upon a few examples and a lot of wishful thinking. In Chapter Two, the authors address errors in arithmetic based mostly upon misunderstandings of notations. Chapter Three deals with algebraic errors primarily caused by inadvertent division by zero or the introduction of extraneous roots. In Chapter Four we have errors in geometric proofs, mostly arising from deliberately misleading diagrams. The final chapter deals with probability, showing mistakes made by confusing the concepts of conditionality, independence, and mutual exclusivity of events. Many of the errors are clever and instructive, some are repetitive and uninteresting; only a few should be designated as "magnificent." VERDICT This volume could be useful to a teacher of mathematics as a source of examples that can hammer home important concepts. Beyond that, it will have a limited readership.—Harold D. Shane, Mathematics, Emeritus, Baruch Coll., CUNY
From the Publisher
“[F]or me it is the mathematical gaffes the rest of us are more likely to fall for that make Posamentier and Lehmann's book interesting. My favourites are the proofs that involve dividing by zero, leading to results such as 1=2.”

-New Scientist

“This volume could be useful to a teacher of mathematics as a source of examples that can hammer home important concepts.”

-Library Journal

“Don’t be scared off by the ‘mathiness’… Magnificent Mistakes in Mathematics is an intriguing read. I’ll bet that even old hands at mathematics will find something new here… a great opportunity as the school year begins, giving us a chance once again to ‘go figure!’”

-Astro Guyz

“A fairly quick and entertaining read for typical math buffs… I think this somewhat unique approach makes the volume a worthwhile, entertaining addition to one's math bookshelf, and it may be particularly useful to secondary school teachers, providing a lot of grist for instructive, thoughtful examples in the classroom.”

-MathTango

“Advanced math skills are not required to enjoy untangling errors that illustrate concepts in arithmetic, algebra, and more.”

-Science News

## Product Details

ISBN-13:
9781616147488
Publisher:
Prometheus Books
Publication date:
08/13/2013
Sold by:
Penguin Random House Publisher Services
Format:
NOOK Book
File size:
6 MB

## Related Subjects

#### MAGNIFICENT MISTAKES IN MATHEMATICS

By Alfred S. Posamentier, Ingmar Lehmann

#### Prometheus Books

ISBN: 978-1-61614-748-8

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Excerpted from MAGNIFICENT MISTAKES IN MATHEMATICS by Alfred S. Posamentier, Ingmar Lehmann. Copyright © 2013 Alfred S. Posamentier and Ingmar Lehmann. Excerpted by permission of Prometheus Books.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

## Meet the Author

Alfred S. Posamentier is dean of the School of Education and professor of mathematics education at Mercy College in Dobbs Ferry, New York. Previously, he had the same positions at the City College of the City University of New York for forty years.  He has published over fifty-five books in the area of mathematics and mathematics education, including The Fabulous Fibonacci Numbers (with Ingmar Lehmann).

Ingmar Lehmann is retired from the mathematics faculty at Humboldt University in Berlin. For many years he led the Berlin Mathematics Student Society for gifted secondary-school students, with which he is still closely engaged today.  He is the coauthor with Alfred S. Posamentier of The Secrets of TrianglesThe Glorious Golden Ratio, and three other books.

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